Manufacturers of filtration devices often offer small scale sizing tools for initial evaluation of process streams and for estimating membrane area requirements for the full scale process. Ideally, small scale devices should contain a minimum of membrane area or filtration media to save test fluid while also scaling linearly with their corresponding large scale devices. However, variability in the performance of small scale devices adds uncertainty to the scale-up requirements, resulting in potentially excessive sizing to guard against the possibility that the tested small scale device(s) represented the low end of the performance distribution.
In the case of microfiltration membrane filters, for example, there are many factors that influence membrane performance, including the pore size distribution, the membrane chemistry, membrane thickness, membrane porosity, and others. While membrane manufacturing processes are designed to control all of these factors to maximize uniformity and consistency, there inevitably will be some distribution within normal manufacturing conditions for all of these variables. This membrane variability limits device-to-device performance consistency and therefore limits the precision to which large scale performance can be predicted from small scale performance.
The performance of either large scale samples or small scale filtration devices is often used to estimate the sizing requirements of large scale devices. The use of small scale devices for sizing provides an obvious economic advantage. For example, in sterile filtration of biological fluids, 47 mm or 25 mm membrane discs offer a convenient format for evaluating performance against the discs to large scale membrane devices (e.g., cartridges containing tens to thousands of times more area). For accurate scale-up, the membrane in the small scale device must be representative of the membrane in the large scale devices. However, as in any manufacturing process, there is a finite tolerance in acceptable performance from one lot of membranes to another. The membrane in a scaling device could originate from anywhere within the acceptable performance range. Accordingly, when estimating the required sizing of full scale devices, the variability in membrane performance must be accounted for, necessitating the use of liberal safety factors in scaling estimates.
This can be illustrated by considering a hypothetical distribution of membrane performances as shown in FIG. 1. In this example, average performance (either permeability or throughput capacity) of all membrane lots is normalized to one and the acceptable range of performance is defined as ±30% of the mean. One commonly employed approach is to use a small scale device containing membrane randomly selected from the population, which could perform at anywhere from 0.7 to 1.3. Similarly, a large scale device could perform at anywhere within the same 0.7 to 1.3 range. When scaling from a small scale to a large scale device, the possibility that the small scale device contains high end (1.3) membrane while the large scale device could contain low end (0.7) membrane must be accounted for. That is, a scaling safety factor of 1.3/0.7=1.86 must be applied to ensure that the large scale device requirements are not undersized (see FIG. 2). In this situation, the worst case performance of the full system will be accurately estimated. However, it is also possible that the small scale device could contain membrane at the low end of the distribution (0.7) while the large scale device contains high end (1.3) membrane. Applying the same safety factor would result in a full system performance of (1/3/0.7)/(0.7/1.3), or 3.45. The result would be a filtration system that is oversized by a factor of 3.45. This value is defined as the scaling factor uncertainty ratio (Usf) according to the following formula (1):Usf=(Fh/Sl)/(Fl/Sh)=(Fh/Fl)*(Sh/Sl)  (1)where Fh is the full scale high end potential performance, Fl is the full scale low end potential performance, Sh is the scaling device high end potential performance, and Sl is the scaling device low end potential performance.
It therefore would be desirable to reduce the range of scaling device performance in order to lower large scale device requirements and save costs.